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On the experimental verification of quantum complexity in linear optics


Quantum computers promise to solve certain problems that are forever intractable to classical computers. The first of these devices are likely to tackle bespoke problems suited to their own particular physical capabilities. Sampling the probability distribution from many bosons interfering quantum-mechanically is conjectured to be intractable to a classical computer but solvable with photons in linear optics. However, the complexity of this type of problem means its solution is mathematically unverifiable, so the task of establishing successful operation becomes one of gathering sufficiently convincing circumstantial or experimental evidence. Here, we develop scalable methods to experimentally establish correct operation for this class of computation, which we implement for three, four and five photons in integrated optical circuits, on Hilbert spaces of up to 50,000 dimensions. Our broad approach is practical for all quantum computational architectures where formal verification methods for quantum algorithms are either intractable or unknown.

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Figure 1: Experimental set-up to generate interfere and detect single photons.
Figure 2: Three-photon data from the RU chip showing verification of boson sampling against the uniform distribution and discrimination between quantum and classical statistics.
Figure 3: The absence and emergence of multimode correlations in the form of bosonic clouds in three-photon correlation cubes for a nine-mode RU and a 21-mode QW.
Figure 4: Experimental verification of correct sampling with bosonic clouding using a QW unitary.


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The authors acknowledge support from the Engineering and Physical Sciences Research Council (EPSRC), the European Research Council (ERC), the Centre for Nanoscience and Quantum Information (NSQI), the US Air Force Office of Scientific Research (AFOSR) and the US Army Research Laboratory (ARL) J.C.F.M. is supported by a Leverhulme Trust Early Career Fellowship. J.L.O.B. acknowledges a Royal Society Wolfson Merit Award and a Royal Academy of Engineering Chair in Emerging Technologies. The authors thank G. Marshall, E. Martín López, A. Peruzzo, A. Politi and A. Rubenok for technical assistance.

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Devices were fabricated by N.I. and K.W. All other authors contributed to the theory, experiments, analysis and writing of the manuscript.

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Correspondence to Jonathan C. F. Matthews or Anthony Laing.

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The authors declare no competing financial interests.

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Carolan, J., Meinecke, J., Shadbolt, P. et al. On the experimental verification of quantum complexity in linear optics. Nature Photon 8, 621–626 (2014).

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